A fuzzy system is an information processing system which consists of fuzzy sets and their associations. Fuzzy sets are defined by membership functions, and associations of fuzzy sets are represented in a form of "if-then" rules. A fuzzy system is typically designed and tuned by a human operator who has the knowledge of a particular system's characteristics and behavior. Since the human operator can represent the system in natural language form, the fuzzy system approach provides an effective means to represent dynamic problems and solutions. Nevertheless, there is a lack of systematic ways to design and tune such systems.
One solution was proposed by Araki, Nomura, Hayashi, and Wakami in their article "A Self-Generating Method of Fuzzy Inference Rules", Proc. IFES, pp. 1047-1058 (1991). The proposed system generates a new membership function at a point of maximum output error. However, the system generates a large number of rules when the number of inputs increases. For instance, consider a 2-input-1-output fuzzy system with 3 membership functions for each of the two input variables. Initially, there are 3.times.3=9 rules as depicted in the FIG. 1A. Under the above-noted methodology, tuning the system generates a new membership function for each input at a point of maximum output error. As a result, the number of rules increases to 4.times.4=16 as shown in FIG. 1B. This synthesis device thereby generates a relatively large number of rules for the provided data.